On the uniqueness of Euclidean distance matrix completions
نویسندگان
چکیده
منابع مشابه
Euclidean distance matrix completion problems
A Euclidean distance matrix is one in which the (i, j) entry specifies the squared distance between particle i and particle j. Given a partially-specified symmetric matrix A with zero diagonal, the Euclidean distance matrix completion problem (EDMCP) is to determine the unspecified entries to make A a Euclidean distance matrix. We survey three different approaches to solving the EDMCP.We advoca...
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The Euclidean distance matrix approximation problem as well as the completion problem have received a lot of attention in recent years because of their many important applications. In contrast to the many interesting but often sophisticated algorithms proposed in the literature, this paper offers a relatively straightforward procedure that can tackle both problems by the same framework. The loc...
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If A is a real symmetric matrix and P is an orthogonal projection onto a hyperplane, then we derive a formula for the Moore-Penrose inverse of PAP . As an application, we obtain a formula for the MoorePenrose inverse of a Euclidean distance matrix (EDM) which generalizes formulae for the inverse of a EDM in the literature. To an invertible spherical EDM, we associate a Laplacian matrix (which w...
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*Correspondence: [email protected] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia Abstract A matrix with zero diagonal is called a Euclidean distance matrix when the matrix values are measurements of distances between points in a Euclidean space. Because of data errors such a matrix may not be exactly Euclidean and it is desira...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00737-1